p and 2p+1 are Sophie Germain primes if and only if p is prime and 2^(2p) == 1 (mod 2p+1). - Vincenzo Librandi, Oct 09 2012

In the spirit of the conjecture related to A217788, we conjecture that for any integers n >= m > 0 there are infinitely many integers b > a(n) such that the number sum_{k=m}^n a(k)*b^(n-k) is prime. - Zhi-Wei Sun, Mar 26 2013